Griezmann, twice, and Olivier Giroud both tested Irish goalkeeper Darren Randolph, as did Pogba with a long-range free-kick.
No quarter was asked or given as things got heated on the pitch with four yellow cards dished out in the first-half.
France coach Didier Deschamps injected some pace after the break by bringing on fleet-footed winger Kingsley Coman for N’Golo Kante.
The French played at a much higher tempo and Randolph was thoroughly tested by Blaise Matuidi’s shot from just outside the box on 55 minutes.
France drew level when Griezmann rose highest to meet Sagna’s pin-point cross on 58 minutes.
Randolph got a glove on the bullet header, but it was destined only for the back of the net.
Griezmann struck again three minutes later when Giroud headed down into the Atletico Madrid winger’s path to slam his shot past Randolph.
With France in top gear, Duffy’s desperate lunge clipped Griezmann’s ankle on the edge of the area and Rizzoli had to show the Irishman the red card on 66 minutes.
Only Irish determination, and a lack of a final touch, prevented Griezmann finishing with a hat-trick.